Tying Light in Knots [Slide Show]

Newfound solutions to Maxwell’s electromagnetism equations show light can get as tangled as a sailor’s rope

William Irvine Lab/University of Chicago

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Knots can help unravel some knotty (sorry!) situations. The mathematical study of knotted shapes has proved constructive for many branches of physics, from understanding how fluids flow to developing quantum computers. Now physicists have found that light itself can be knotted by discovering a new set of solutions to the famous Maxwell equations of electromagnetism.

In the 1860s Scottish physicist James Clerk Maxwell wrote down a series of equations describing how electric and magnetic fields form and change. These foundational formulas, still printed in almost every physics textbook, led to the crucial realization that light is an electromagnetic phenomenon. “They are everything you need to know about light and everything you need to know about the interaction of light with matter,” says University of Chicago physicist William Irvine. Irvine’s graduate student Hridesh Kedia led the study, which was published October 11 in Physical Review Letters.

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The researchers worked out a family of solutions to Maxwell’s equations that represent beams of light whose structure is knotted. Thanks to Maxwell, light is known to be an electromagnetic wave—an oscillating electric and magnetic field. To the casual observer knotted light would appear normal, but embedded inside it are electromagnetic field lines tied up in knots. “What they’ve done is shown a new sort of way that those fields can behave,” says Mark Dennis, a physicist at the University of Bristol in England who was not involved in the research. “No one had worked out the details or even quite suggested the possibility that the laws of nature allow for electromagnetic fields to take these shapes.” The fact that light can be knotted reveals new subtleties about the nature of light itself and the fields that underlie it. “Most people would say we understand how Maxwell’s equations work,” Irvine says. “But one of the things I think is remarkable is that you can have such an elegant and complex structure within what is known as a simple theory.”

Knots are not (get it?) just random structures. They are abundant in nature—from knotted strands of DNA molecules to the liquid crystals inside computer monitors to the strands of plasma in the sun’s atmosphere. Studying the mathematics and topology of knots can unlock the secrets of many three-dimensional processes. “Somehow the fact that knotted curves can exist in three dimensions is something special about three-dimensional space,” Dennis says. Knots are essential for understanding the way particles flow and twist back on themselves in a three-dimensional fluid, for example.

Knotted light isn’t merely a theoretical possibility. Scientists could create laser beams that realize the newfound mathematical solutions with fairly uncomplicated modifications to existing laboratory equipment, Irvine says. Doing so might allow physicists to produce knotted versions of materials called Bose–Einstein condensates, where gas atoms condense under extremely cold temperatures, or to induce knots in trapped plasma. “This could lead to improved understanding of natural plasmas like the sun as well as engineering plasmas for the production of energy,” Irvine says. Knots might be (wait for it) just the way to tie new ideas together.

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